If the product of two of the roots of x⁴ – 5x³ + 5x² + 5x – 6 = 0 is 3 then the roots are

x⁴ – 5x³ + 5x² + 5x – 6 = 0

$$\begin{gathered} \alpha ,\beta ,\gamma ,\delta are roots of the equation then, \\ {S}_1\Rightarrow \alpha +\beta +\gamma +\delta =5 \\ {S}_2\Rightarrow \alpha \beta +\alpha \gamma +\alpha \delta +\beta \gamma +\beta \delta +\gamma \delta =5 \\ {S}_3\Rightarrow \alpha \beta \gamma +\alpha \beta \delta +\alpha \gamma \delta +\beta \gamma \delta =-5 \\ {S}_4\Rightarrow \alpha \beta \gamma \delta =-6 \\ \text{ Assuming }\alpha \beta =3{\text{ then from S}}_4 \\ \gamma \delta =-2 \\ from S_3 \\ 3(\gamma +\delta )-2(\alpha +\beta )=-5 ···\left(1\right) \\ from S_1 \\ (\gamma +\delta )+(\alpha +\beta )=5 ···\left(2\right) \\ Solving \left(1\right) and \left(2\right) will get, \\ \alpha +\beta =4 ,\gamma +\delta =1 \\ Now, \\ \alpha +\beta =4,\alpha \beta =3\text{ and γ}+\delta =1,\gamma \delta =-2 \\ then the roots are \\ -1,1,2,3 \end{gathered}$$